mem_fixingSubgroup_compl_iff_movedBy_subset

English

Membership in fixingSubgroup M sᶜ is characterized by a moved-by subset relation: (fixedBy α m)ᶜ ⊆ s.

Русский

Членство в fixingSubgroup M sᶜ характеризуется relation moved-by: (fixedBy α m)ᶜ ⊆ s.

LaTeX

$$$m \\in fixingSubgroup(M,s^c) \\iff (fixedBy(\\alpha,m))^c \\subseteq s$$$

Lean4

@[to_additive]
theorem mem_fixingSubgroup_compl_iff_movedBy_subset {s : Set α} {m : M} :
    m ∈ fixingSubgroup M sᶜ ↔ (fixedBy α m)ᶜ ⊆ s := by rw [mem_fixingSubgroup_iff_subset_fixedBy, Set.compl_subset_comm]

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